| 摘要: |
| 设R和S是环，ψ：R → S是强可分扩张.本文研究了（Gorenstein）整体维数和表示型在R与S之间的关系.利用同调方法，证明了（1）R与S有相同的左整体维数，左弱整体维数，左Gorenstein整体维数；（2）若R和S是阿丁代数，则R是CM-有限的（CM-自由的，有限表示型）当且仅当S是CM-有限的（CM-自由的，有限表示型），推广了已知的结果. |
| 关键词: 强可分扩张 左Gorenstein整体维数 CM-有限的 |
| DOI： |
| 分类号:O154.2 |
| 基金项目:Supported by Supported by National Natural Science Foundation of China (11401339); NSF of Shandong Province of China (ZR2014AQ024); Youth Foundation and Doctor's Initial Foundation of Qufu Normal University (Xkj201401; BSQD2012042). |
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| NOTES ON STRONGLY SEPARABLE EXTENSIONS |
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XU Ai-min
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School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
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| Abstract: |
| Let R and S be rings and ψ:R → S a strongly separable extension. In this paper, we study the relationship of (Gorenstein) global dimensions and representation type between R and S. By using the homological methods, we proved that (1) R and S have the same left global dimension, left weak global dimension, left Gorenstein global dimension; (2) Assume that R and S are Artin algebras, then R is CM-finite (resp., CM-free, of finite representation type) if and only if so is S, which generalize some known results. |
| Key words: strongly separable extension left Gorenstein global dimension CM-finite |
